Sampled paths in Monte Carlo ray tracing can be arbitrarily close to each other due to its stochastic nature. Such clumped samples in the path space tend to contribute little toward an accurate estimate of each pixel. Bidirectional light transport methods make this issue further complicated since connecting paths of sampled subpaths can be arbitrarily clumped again. We propose a matrix formulation of bidirectional light transport that enables stratification (and low-discrepancy sampling) in this connection space. This stratification allows us to distribute computation evenly across contributing paths in the image, which is not possible with standard bidirectional or Markov chain solutions. Each element in our matrix formulation represents a pair of connected eye- and light-subpaths. By carefully reordering these elements, we build a 2D space where equally contributing paths are distributed coherently. We devise an unbiased rendering algorithm that leverages this coherence to effectively sample path space, consistently achieving a 2 − 3 x speedup in radiometrically complex scenes compared to the state-of-the-art.

Monte Carlo ray tracing has become ubiquitous in most commercial renderers and in custom shaders used for visual effects and feature animation. But many advanced Monte Carlo algorithms are not widely used and are often misunderstood. In this course, attendees learn about the practical aspects of variance-reduction methods with a focus on all variants of importance sampling. The course also covers quasi-Monte Carlo methods at the industry level, as well as the practical aspects of bidirectional path tracing combined with multiple importance sampling and Metropolis Light Transport. Practical advice is provided throughout the course.

Realistic rendering of outdoor terrain requires both that the geometry of the environment be modeled accurately and that appropriate texturing be laid down on top of that geometry. While elevation data is widely available for much of the world and many methods exist for converting this data to forms suitable for graphics systems, we have much less experience with patterning the resulting surface. This paper describes an approach for using panchromatic (grayscale) aerial imagery to produce color views of alpine scenes. The method is able to remove shading and shadowing effects in the original image so that shading and shadowing appropriate to variable times of day can be added. Seasonal snow cover can be added in a physically plausible manner. Finally, 3-D instancing of trees and brush can be added in locations consistent with the imagery, significantly improving the visual quality.

Increased demand for global illumination, image based-lighting and simplified workflow have pushed raytracing into mainstream. Many rendering and simulation algorithms that were considered strictly offline are becoming more interactive on massively parallel GPUs. Unfortunately, the amount of available memory on modern GPUs is relatively small. Scenes for feature film rendering and visualization have large geometric complexity and can easily contain millions of polygons and a large number of texture maps and other data attributes. In this talk, we describe a general purpose out-of-core ray tracing engine for the GPU where we address data management, ray-intersection and shading. We utilize a GPU data cache that enables efficient access of out-of-core data. We develop a novel ray intersection algorithm built around acceleration structure that brings needed data on demand using page-swapping. We further reduce memory usage by using a simple geometry quantization. The ray tracing engine is used to implement a variety of rendering and light transport algorithms.

The bidirectional reflectance distribution function (BRDF) formalism is commonly used in computer graphics to represent surface reflection properties. Although many BRDF models have been proposed, most do not possess at least some of the desirable practical properties. In this paper we present a simple and flexible model which satisfies many of these requirements. We show that the proposed model provides a good approximation for many real world materials, obeys basic physical restrictions, allows straightforward hardware implementation and provides for efficient sampling in a Monte-Carlo rendering system. A procedure to fit the model to BRDF measurement data is presented which suggests a simplified way of measuring surface reflection.

The most straightforward image synthesis algorithm is to follow photon-like particles from luminaires through the environment. These particles scatter or are absorbed when they interact with a surface or a volume. They contribute to the image if and when they strike a sensor. Such an algorithm implicitly solves the light transport equation, Alternatively, adjoint photons can be traced from the sensor to the luminaires to produce the same image. This "adjoint photon" tracing algorithm is described, and its strengths and weaknesses are discussed, as well as details needed to make adjoint photon tracing practical.

Natural scenes contain large amounts of geometry, such as hundreds of thousands or even millions of tree leaves and grass blades. Subtle lighting effects present in such environments usually include a significant amount of occlusion effects and lighting variation. These effects are important for realistic renderings of such natural environments; however, plausible lighting and full global illumination computation come at prohibitive costs especially for interactive viewing. As a solution to this problem, we present a simple approximation to integrated visibility over a hemisphere (ambient occlusion) that allows interactive rendering of complex and dynamic scenes. Based on a set of simple assumptions, we show that our method allows the rendering of plausible variation in lighting at modest additional computation and little or no precomputation, for complex and dynamic scenes.

Efficient and visually compelling reproduction of effects due to multiple scattering in participating media remains one of the most difficult tasks in computer graphics. Although several fast techniques were recently developed, most of them work only for special types of media (for example, uniform or sufficiently dense) or require extensive precomputation. In this paper we present a lighting model for the general case of inhomogeneous medium and demonstrate its implementation on programmable graphics hardware. It is capable of producing high quality imagery at interactive frame rates with only mild assumptions about medium scattering properties and a moderate amount of simple precomputation.

Volumetric light transport effects are significant for many materials like skin, smoke, clouds, snow or water. In particular, one must consider the multiple scattering of light within the volume. While it is possible to simulate such media using volumetric Monte Carlo or finite element techniques, those methods are very computationally expensive. On the other hand, simple analytic models have so far been limited to homogeneous and/or optically dense media and cannot be easily extended to include strongly directional effects and visibility in spatially varying volumes. We present a practical method for rendering volumetric effects that include multiple scattering. We show an expression for the point spread function that captures blurring of radiance due to multiple scattering. We develop a general framework for incorporating this point spread function, while considering inhomogeneous media - this framework could also be used with other analytic multiple scattering models.

Volume rendering is a flexible technique for visualizing dense 3D volumetric datasets. A central element of volume rendering is the conversion between data values and observable quantities such as color and opacity. This process is usually realized through the use of transfer functions that are precomputed and stored in lookup tables. For multidimensional transfer functions applied to multivariate data, these lookup tables become prohibitively large. We propose the direct evaluation of a particular type of transfer functions based on a sum of Gaussians. Because of their simple form (in terms of number of parameters), these functions and their analytic integrals along line segments can be evaluated efficiently on current graphics hardware, obviating the need for precomputed lookup tables. We have adopted these transfer functions because they are well suited for classification based on a unique combination of multiple data values that localize features in the transfer function domain. We apply this technique to the visualization of several multivariate datasets (CT, cryosection) that are difficult to classify and render accurately at interactive rates using traditional approaches.

Simulating the transport of light in volumes such as clouds or objects with subsurface scattering is computationally expensive. We describe an approximation to such transport using path integration. Unlike the more commonly used diffusion approximation, the path integration approach does not explicitly rely on the assumption that the material within the volume is dense. Instead, it assumes the phase function of the volume material is strongly forward scattering and uniform throughout the medium, an assumption that is often the case in nature. We show that this approach is useful for simulating subsurface scattering and scattering in clouds.

Due to our familiarity with how fluids move and interact, as well as their complexity, plausible animation of fluids remains a challenging problem. We present a particle interaction method for simulating fluids. The underlying equations of fluid motion are discretized using moving particles and their interactions. The method allows simulation and modeling of mixing fluids with different physical properties, fluid interactions with stationary objects, and fluids that exhibit significant interface breakup and fragmentation. The gridless computational method is suited for medium scale problems since computational elements exist only where needed. The method fits well into the current user interaction paradigm and allows easy user control over the desired fluid motion.

An object's appearance is affected both by light reflecting from its surface and light propagating through its volume. Simulating such light-object interaction is necessary when creating realistic computer graphics images. While for some objects surface reflection dominates, for many objects multiple scattering within the volume contributes significantly to visual appearance. Since the effects of multiple scattering are very costly to compute and simulate, we describe several approximations for light transport in volumetric materials that are especially applicable for depiction of natural materials such as water and clouds. These approximations differ by assuming different levels of complexity in the medium being approximated. First, the object is assumed to be a uniform body of water illuminated from above. Here the specificity of geometry and material composition can be leveraged to yield a very efficient approximation. Second, the object is allowed to be composed of layers of varying optical properties, and the object's geometry is of low curvature relative to the layer thickness. Finally, the general case of geometry and optical properties are assumed and the mathematical tool of path integrals is used to develop approximations that characterize the path that contributes the most to the final intensity and give a solution in terms of the most probable path and quadratic fluctuations around this path. A hierarchical version of this approximation is also developed. All of these methods approximate the appearance of light transport within the volume of materials equation with different assumptions ranging from a very specific medium to very general materials that can be applied to a variety of rendering problems. These methods provide insights into light propagation that could lead to further approximations that are tailored to the amount of generality of particular problems.

Direct volume rendering is a commonly used technique in visualization applications. Many of these applications require sophisticated shading models to capture subtle lighting effects and characteristics of volumetric data and materials. For many volumes, homogeneous regions pose problems for typical gradient-based surface shading. Many common objects and natural phenomena exhibit visual quality that cannot be captured using simple lighting models or cannot be solved at interactive rates using more sophisticated methods. We present a simple yet effective interactive shading model which captures volumetric light attenuation effects that incorporates volumetric shadows, an approximation to phase functions, an approximation to forward scattering, and chromatic attenuation that provides the subtle appearance of translucency. We also present a technique for volume displacement or perturbation that allows realistic interactive modeling of high frequency detail for both real and synthetic volumetric data.

Direct volume rendering is a commonly used technique in visualization applications. Many of these applications require sophisticated shading models to capture subtle lighting effects and characteristics of volumetric data and materials. Many common objects and natural phenomena exhibit visual quality that cannot be captured using simple lighting models or cannot be solved at interactive rates using more sophisticated methods. We present a simple yet effective interactive shading model which captures volumetric light attenuation effects to produce volumetric shadows and the subtle appearance of translucency. We also present a technique for volume displacement or perturbation that allows realistic interactive modeling of high frequency detail for real and synthetic volumetric data.

Subsurface scattering and light transport in volumetric media are critical to achieve a realistic depiction of a material. We describe several analytical approximations and methods for volumetric light transport in media of various optical properties that are efficient and easy to compute. Most natural materials exhibit a sudden surge in brightness called the opposition effect around the zero phase angle, where incident and viewing directions coincide. We present an approximation to the opposition effect in a particulate medium using a few physically realistic mathematical approximations. These analytical approximations can be used as tools or as a starting point for modeling the appearance of complex volumetric materials such as biological materials (skin, leaves) or inorganic materials (snow, clouds, rocks, paint). We demonstrate these approximations for several natural materials that exhibit substantial volumetric light transport and show how to use them to model complex materials.

This paper presents a physically-based model of the night sky for realistic image synthesis. We model both the direct appearance of the night sky and the illumination coming from the Moon, the stars, the zodiacal light, and the atmosphere. To accurately predict the appearance of night scenes we use physically-based astronomical data, both for position and radiometry. The Moon is simulated as a geometric model illuminated by the Sun, using recently measured elevation and albedo maps, as well as a specialized BRDF. For visible stars, we include the position, magnitude, and temperature of the star, while for the Milky Way and other nebulae we use a processed photograph. Zodiacal light due to scattering in the dust covering the solar system, galactic light, and airglow due to light emission of the atmosphere are simulated from measured data. We couple these components with an accurate simulation of the atmosphere. To demonstrate our model, we show a variety of night scenes rendered with a Monte Carlo ray tracer.

The Metropolis Light Transport algorithm is a variant of the classic Metropolis method used in statistical physics. A variance analysis of the Metropolis Light Transport algorithm is presented that bounds its variance in terms of the number of paths used and the intrinsic correlation between samples. It is shown that the variance of a pixel is Θ(1/N), where N is the number of samples for the entire image. The analysis uses basic probability, Bayes’ law, and the principle of stationary distributions. This result implies that the presence of correlation in the algorithm does not make its asymptotic time complexity worse than uncorrelated Monte Carlo methods such as path tracing.